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@Paul661
I'm not sure if You know how this Superhost-system works.
The superhost badge is not related to a listing but to the host who runs the listing. If a host runs 7 listings and one of the listings meets the requirements to become superhost, then the Superost-badge is shown on all of the 7 listing of the host. Why? Because they are run by a superhost. That explains why there are listings with only 3 reviews but do show the badge.
You wrote:
Why do You assume that it's the Superhost badge that moves these listings up in search results? Where does it say that this is the case? Even airbnb themselves do not state that the badge would move listings up in search.
If You're not familiar with the positioning in search results, pls read this thread:
https://community.withairbnb.com/t5/Host-Circle/Let-s-talk-about-search/m-p/1346232#M14385
The thread has 6 pages, read them all and You'll understand.